HSS(0)：一种改进的厄米特/反厄米特分裂迭代法
数值分析
2021-09-30 v2 数值分析
摘要
我们提出了厄米特/反厄米特分裂（HSS）迭代法的一个改进版本，称之为HSS(0)，用于求解厄米特部分正定的非厄米特线性系统。该改进基于无位移地求解厄米特半步迭代，并仅对反厄米特求解应用位移。解析导出了一个最优参数，并获得了相应的收敛速度上界。通过解析证明与数值验证相结合，我们表明HSS(0)比标准HSS收敛速度快得多。此外，HSS(0)对参数选取的敏感性大幅降低。二维与三维对流扩散模型问题的数值实验说明了HSS(0)的高效性。
引用
@article{arxiv.2109.13327,
title = {HSS(0): an Improved Hermitian/Skew-Hermitian Splitting Iteration},
author = {Chen Greif and Yunhui He},
journal= {arXiv preprint arXiv:2109.13327},
year = {2021}
}
备注
After posting this paper, we found out that the proposed method had already been published previously. See Li, Huang, and Liu, Numerical Linear Algebra with Applications, 14 (2007), pp. 217-235; Salkuyeh and Behnejad, Numerical Linear Algebra with Applications, 19 (2012), pp. 885-890